percentage change

Learning Objective:

• we are learning to make a percentage increase or decrease on an amount.
• as an extension, a harder skill is to find the original amount when you know the amount after a percentage change.

Investing:

• This is useful because
  • very often in life you will see items in sale with a certain percentage off the original price
  • in many countries and states goods are sold with an added 'sales tax' or VAT (value added tax)
  • you may be offered a percentage increase in your pay
  • you will pay a percentage of your pay in income tax
  • 
    
• A functional (real-life) application is...
• This skill leads to...
• A 'free gift' with this skill is that we can now also...
• This could help you if you want to work in...

Preparing:

• Are we ready? Can you already... ?
• Let's be sure you can...
• Before you start you need to know:
• You will have a deeper understanding if you also know:

Discovering:

• What has this purple porcupine got to do with percentage change?

• you might like to have a bitmap of this picture to play with

percentage porcupine.bmp

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• Here's someone using a percentage porcupine. How do they use it to solve the problem?

Percentage Porcupine.jnt

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• 410 KB

• Try to predict the next one aloud or on a mini-whiteboard.
• Investigate...

Modeling:

• Here are some examples of people getting it right:
• Here are some examples of people getting it wrong in typical ways:
• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• One way to reduce something by 20% is to find 10% first by dividing by 10 and then use the fact that 20% is double 10%. Once you've found 20% take it off the original. This is the 'percentage porcupine' method illustrated above. It's easy, but it's slow.
  
  
• Another approach might be to think of 20% as the fraction 20/100. Since this cancels down to 1/5 you could divide your amount by 5 to find 20%. Once you've got that, subtract as before.
  
  
• A useful shortcut is to realise that 30% off leaves 80% left. Since 80% is equivalent to 0.8, to find 20% off something you can simply multiply your amount by 0.8. This is by far the quickest method.
  
  
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practising:

• Okay, I know it makes me a bit weird, but when I see a sale in a furniture shop, the first thing I think is: "Wow! There's got to be some good maths in that!"
• So, thinking of you, when Habitat went bankrupt in the UK a few years ago and advertised a 20% off everything sale, I got out my mobile phone and took this video:

• I'm happy for you to make up any maths questions you like from this. The more the better, but here are some to get you started:

1. They claimed 20% off everything. I'm not so sure they got that right. Here's a screenshot from 0:06 showing the prices of some sofas:
   
   I think we can assume that the first column of figures is the sale price and the second column is the original price.
   Which sale prices are correct and which aren't?
2. What should the sale prices for the five items be?
   
   
3. Work out the ×percentage discount on each item.
   
   
4. Which items represent the biggest bargain?
   
   
5. 
   

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...